Covariant Color-Kinematics Duality

Abstract

We show that color-kinematics duality is a manifest property of the equations of motion governing currents and field strengths. For the nonlinear sigma model (NLSM), this insight enables an implementation of the double copy at the level of fields, as well as an explicit construction of the kinematic algebra and associated kinematic current. As a byproduct, we also derive new formulations of the special Galileon (SG) and Born-Infeld (BI) theory. For Yang-Mills (YM) theory, this same approach reveals a novel structure -- covariant color-kinematics duality -- whose only difference from the conventional duality is that $1/\square$ is replaced with covariant $1/D^2$. Remarkably, this structure implies that YM theory is itself the covariant double copy of gauged biadjoint scalar (GBAS) theory and an $F^3$ theory of field strengths encoding a corresponding kinematic algebra and current. Directly applying the double copy to equations of motion, we derive general relativity (GR) from the product of Einstein-YM and $F^3$ theory. This exercise reveals a trivial variant of the classical double copy that recasts any solution of GR as a solution of YM theory in a curved background. Covariant color-kinematics duality also implies a new decomposition of tree-level amplitudes in YM theory into those of GBAS theory. Using this representation we derive a closed-form, analytic expression for all BCJ numerators in YM theory and the NLSM for any number of particles in any spacetime dimension. By virtue of the double copy, this constitutes an explicit formula for all tree-level scattering amplitudes in YM, GR, NLSM, SG, and BI.

arXiv comment54 pages, 2 figures, 2 ancillary files. v2 added references

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Cited by in corpus (22)

• Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Celestial chiral algebras, colour-kinematics duality and integrability
• Double Field Theory as the Double Copy of Yang-Mills
• Kinematic Lie Algebras From Twistor Spaces
• Asymptotic Weyl Double Copy
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• 10D Super-Yang-Mills Scattering Amplitudes From Its Pure Spinor Action
• Amplitudes, Hopf algebras and the colour-kinematics duality
• The double copy of the multipole expansion
• Towards Color-Kinematics Duality in Generic Spacetimes
• Non-perturbative aspects of the self-dual double copy
• Non-perturbative Double Copy in Flatland
• Kinematic Hopf algebra for amplitudes and form factors
• Universal expansions of scattering amplitudes for gravitons, gluons and Goldstone particles
• Homotopy double copy and the Kawai-Lewellen-Tye relations for the non-abelian and tensor Navier-Stokes equations
• Flavour-kinematics duality for Goldstone modes
• Covariant color-kinematics duality, Hopf algebras and permutohedra
• Perturbations of General Relativity to All Orders and the General $n^{\mathrm{th}}$ Order Terms
• New relations for tree-level form factors and scattering amplitudes
• Color-Kinematics Relation from the Feynman Diagram Perspective
• NS-NS Spacetimes from Amplitudes